Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals

Valery S. Gordon; F. Werner; O. A. Yanushkevich

RAIRO - Operations Research (2010)

  • Volume: 35, Issue: 1, page 71-83
  • ISSN: 0399-0559

Abstract

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This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O(nlogn) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.

How to cite

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Gordon, Valery S., Werner, F., and Yanushkevich, O. A.. "Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals." RAIRO - Operations Research 35.1 (2010): 71-83. <http://eudml.org/doc/197794>.

@article{Gordon2010,
abstract = { This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O(nlogn) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights. },
author = {Gordon, Valery S., Werner, F., Yanushkevich, O. A.},
journal = {RAIRO - Operations Research},
keywords = {Single machine scheduling; release and due dates; deadlines; number of late jobs.; single machine scheduling; deadlines; number of late jobs},
language = {eng},
month = {3},
number = {1},
pages = {71-83},
publisher = {EDP Sciences},
title = {Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals},
url = {http://eudml.org/doc/197794},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Gordon, Valery S.
AU - Werner, F.
AU - Yanushkevich, O. A.
TI - Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 71
EP - 83
AB - This paper is devoted to the following version of the single machine preemptive scheduling problem of minimizing the weighted number of late jobs. A processing time, a release date, a due date and a weight of each job are given. Certain jobs are specified to be completed in time, i.e., their due dates are assigned to be deadlines, while the other jobs are allowed to be completed after their due dates. The release/due date intervals are nested, i.e., no two of them overlap (either they have at most one common point or one covers the other). Necessary and sufficient conditions for the completion of all jobs in time are considered, and an O(nlogn) algorithm (where n is the number of jobs) is proposed for solving the problem of minimizing the weighted number of late jobs in case of oppositely ordered processing times and weights.
LA - eng
KW - Single machine scheduling; release and due dates; deadlines; number of late jobs.; single machine scheduling; deadlines; number of late jobs
UR - http://eudml.org/doc/197794
ER -

References

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  2. V.S. Gordon and V.S. Tanaev, Single machine deterministic scheduling with step functions of penalties, in: Computers in Engineering. Minsk (1971) 3-8 (in Russian).  
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  10. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling: Algorithms and complexity, edited by S.C. Graves, A.H.G. Rinnooy Kan and P.H. Zipkin, Logistics of Production and Inventory. North-Holland, Handbooks Oper. Res. Management Sci.4 (1993) 445-522.  
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  13. J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems. Ann. Discrete Math.1 (1977) 343-362.  Zbl0353.68067
  14. C.L. Monma, Linear-time algorithms for scheduling on parallel processors. Oper. Res.30 (1980) 116-124.  Zbl0481.90048
  15. J.M. Moore, An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci.15 (1968) 102-109.  Zbl0164.20002
  16. J.B. Sidney, An extension of Moore's due date algorithm, edited by S.E. Elmaghraby, Symposium on the Theory of Scheduling and its Applications. Springer, Berlin, Lecture Notes in Econom. and Math. Systems86 (1973) 393-398.  Zbl0273.90032
  17. V.S. Tanaev and V.S. Gordon, On scheduling to minimize the weighted number of late jobs. Vestsi Akad. Navuk Belarus Ser. Fizi.-Mat. Navuk6 (1983) 3-9 (in Russian).  
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